Momentum/Energy Conservation problem

In summary, a massless spring with a spring constant of 20 N/m is placed between two carts with masses of 5 kg and 3.5 kg. After being compressed 1.2 m, the spring pushes the carts apart. To find their speeds, the equations for conservation of energy and momentum can be used, with the potential energy of the spring being .5k(x^2). The force acting on the carts can be determined from the spring constant and the distance compressed.
  • #1
quatli
2
0
Exploding Spring

A massless spring of spring constant 20 N/m is placed between two carts. Cart 1 has a mass M1 = 5 kg and Cart 2 has a mass M2 = 3.5 kg. The carts are pushed toward one another until the spring is compressed a distance 1.2 m. The carts are then released and the spring pushes them apart. After the carts are free of the spring, what are their speeds?

Im sorry but I am utterly confused by this problem.. I am pretty sure that I must first use conservation of energy to find momentum then conservation of momentum to find velocity. Exactly how I apply all these concepts together is scrambling my brain..

please help! :cry:
 
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  • #2
Start with a fbd showing the spring compressed and the spring force (the same force) acting on both carts. Do you know, or can you derive, the potential energy equation for a spring?

The energy stored in the compressed spring will equale the energy of motion for the carts. You know the force acting on the carts, the masses on the carts, and the initial enerty stored in the system.

Good luck.
 
  • #3
The equation for the potential energy of a spring is .5k(x^2), with k being the spring constant and x distance compressed.

Sorry faust9 but i don't think your method will work because I do not have the force acting on the carts. You must have been looking at the spring constant and assumed that was the force. Thanks very much for the help though, any more suggestions would be GREATLY appreciated!

This homework is due in 3 hours and this problem is just killing me! Anyone else have any idea how to tackle it?
 
  • #4
quatli said:
The equation for the potential energy of a spring is .5k(x^2), with k being the spring constant and x distance compressed.

Sorry faust9 but i don't think your method will work because I do not have the force acting on the carts. You must have been looking at the spring constant and assumed that was the force. Thanks very much for the help though, any more suggestions would be GREATLY appreciated!

This homework is due in 3 hours and this problem is just killing me! Anyone else have any idea how to tackle it?

You DO have the force acting on the carts. Reread the question you started this thread with.
 

1. What is momentum conservation?

Momentum conservation is the principle that states that the total momentum of a closed system remains constant over time, regardless of any external forces acting on the system.

2. How is momentum calculated?

Momentum is calculated by multiplying an object's mass by its velocity. The formula for momentum is p = m * v, where p is momentum, m is mass, and v is velocity. Momentum is measured in units of kg*m/s.

3. What is energy conservation?

Energy conservation is the principle that states that energy cannot be created or destroyed, only transferred or converted from one form to another. In other words, the total amount of energy in a closed system remains constant.

4. How is energy calculated?

The formula for calculating energy depends on the type of energy being considered. For kinetic energy, the formula is KE = 1/2 * m * v^2, where KE is kinetic energy, m is mass, and v is velocity. For potential energy, the formula is PE = m * g * h, where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is the height of the object. Energy is measured in units of joules (J).

5. How are momentum and energy related?

Momentum and energy are related through the principle of conservation of energy. In a closed system, the total amount of energy (kinetic and potential) remains constant, so any changes in the momentum of an object must be accompanied by a corresponding change in its energy. This means that as an object gains momentum, its kinetic energy also increases.

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